1. Field of the Invention
The invention relates to the field of detection and monitoring and specifically to a system and method for measuring the characteristics of continuous medium and/or localized targets in a predetermined volume using multiple sensors.
2. Description of the Related Art
An important problem in the field of detection and monitoring is accurately and reliably measuring as many characteristics of a monitored object as possible. Adequate accuracy and reliability are especially important in the case of remote detection and monitoring under adverse measurement conditions. Characteristics of a monitored object produced by detection and monitoring equipment seldom represent the final product of a measurement system. Typically these characteristics are further interpreted for making decisions and/or recommendations and the decisions and/or recommendations are presented to the system's users. By reliably and accurately measuring more characteristics of the monitored object, one ensures more robust and definite decision making and significantly decreases the probability of making an incorrect decision. Best possible data interpretation is especially important for automated real-time systems.
The monitored object can be a predetermined volume in a continuous medium such as the atmosphere, lakes, rivers, the ocean, surface and subsurface terrain, the human body, a chemical reactor, or any other media. Measured characteristics of such medium in a specified volume are used, for example, in the fields of meteorology, weather forecasting, geology, agriculture, medicine, and astronomy. Additionally, measured characteristics of such medium in a specified volume are also used, for example, in monitoring the airspace around airports, in monitoring conditions in chemical and processing plants, and in monitoring other somewhat similar processes and physical configurations. Monitored objects can also be specified targets located in a predetermined volume, such as, missiles, airplanes, obstacles, defects in a product, intruders, or other specified targets; in these cases the measured characteristics of the targets are used for purposes of national defense and homeland security, collision avoidance, non-destructive product testing, business and personal protection, and the like. It should be noted that in the instant disclosure the general term “monitored object” can be construed to refer to a predetermined volume in a continuous medium or a specified target in a predetermined volume. When a specified target is located in a predetermined volume it may also be referred to as a localized target.
Existing monitoring equipment can be divided into two classes namely, single sensor equipment and multiple sensor equipment. Single sensor equipment, such as, for example, standard single-receiver Doppler radars and individual pressure, temperature or other in-situ probes have been and are still widely used for numerous applications. However, such equipment provides a relatively small amount of initial information about the monitored object. This factor significantly limits the number of characteristics of the object that can be determined and also limits the accuracy and reliability of measurements, especially at adverse conditions. Manufacturing and implementing multiple sensor monitoring equipment capable of performing real-time operations is now possible because of the outstanding progress in electronics and computer technologies that has been made during the last several decades. When compared with single sensor monitoring equipment, multiple sensor monitoring equipment provide a dramatically larger amount of initial information about the monitored object and therefore, enable more reliable measurement of a greater number of characteristics of the monitored object with a much higher accuracy under any conditions. Known examples of multiple sensor configurations include arrays of receiving antennas used in spaced antenna radars, arrays of microphones used for underground exploration or for detecting airplane wake vortices, and arrays of in-situ temperature probes used for measuring characteristics of convective or reacting flows.
Monitoring equipment that obtains signals from multiple sensors produces a large amount of initial information about a monitored object in comparison to the information produced with equipment that obtains signals from only a single sensor. The objective of data analysis is to accurately and reliably extract as many useful characteristics of the object as possible. All data processing methods using data obtained from multiple sensors are basically similar in that they utilize the same initial information: a time series of signals from a plurality of sensors. The methods differ by the mathematical functions used for analyzing the signals, the mathematical models for relating these functions to the characteristics of the monitored object, and the assumptions that are adopted for constructing the models.
Traditional correlation function and spectra-based data processing methods for multiple sensor monitoring equipment have been widely used for decades in numerous areas of applications. At the same time, the drawbacks of these methods have been well recognized and thoroughly documented. They are as follows: (1) a poor temporal and/or spatial resolution; (2) the inability to operate in adverse measurement conditions such as external interference and strong clutter; (3) a low reliability of measurements due to the adoption of inappropriate, often too restrictive assumptions, and (4) a limitation in the number of characteristics of the monitored object that can be retrieved. For example, the variance of the vertical turbulent velocity is the only characteristic of atmospheric turbulence that can be retrieved with a spaced antenna profiler using traditional data processing methods.
Drawbacks of traditional data processing methods described hereinabove have been partly addressed by the structure function-based method. In the particular case of a spaced antenna profiler, using structure functions allows an improvement of temporal resolution, the mitigation of external interference and clutter effects, the determination of the variances of the horizontal turbulent velocities and the horizontal momentum flux, and the derivation of operational equations by making a smaller number of less restrictive assumptions. Notwithstanding, the limitations of the structure function-based method have also been well recognized.
To understand the limitations, one should consider the definition and interpretation of structure functions for the received signals s({right arrow over (x)}1,t) and s({right arrow over (x)}2,t) from two sensors in close spatial locations {right arrow over (x)}1 and {right arrow over (x)}2 at two close times t1 and t2. The cross structure function of the order p is defined as follows:Dp({right arrow over (x)},δ{right arrow over (x)},t,τ)=<Δsp({right arrow over (x)},δ{right arrow over (x)},t,τ)>, Δs({right arrow over (x)},δ{right arrow over (x)},t,τ)=s({right arrow over (x)},t)−s({right arrow over (x)}+δ{right arrow over (x)},t+τ)   (1)Hereinafter: t is time, {right arrow over (x)}={right arrow over (x)}1, t=t1, δ{right arrow over (x)}={right arrow over (x)}2−{right arrow over (x)}1 and τ=t2−t1 are respectively the spatial separation between the sensors and the temporal separation between the signals, and the angular brackets < > denote ensemble averages. It is important that equation (1) defines only one equation of order p for a pair of sensors. One can see that Dp({right arrow over (x)},δ{right arrow over (x)},t,τ) is the pth order statistical moment of the increment Δs({right arrow over (x)},δ{right arrow over (x)},t,τ); the latter is customarily interpreted as a band-pass filter extracting fluctuations with spatial and temporal scales |δ{right arrow over (x)}| and τ, respectively. However, it has long been established that this is not the case and that the increment is, in fact, a multi-band filter. For example, the normalized spectral transfer function of the auto increment Δs({right arrow over (x)},0,t,τ)=s({right arrow over (x)},t)−s({right arrow over (x)},t+τ) is 1−cos(2π f τ) with maxima occurring at multiple frequencies f=1/(2τ)+k/τ, k=0, 1, 2, . . . . Customarily, only the first band at k=0 is taken into account in the interpretation of structure functions, while others of the same intensity and bandwidth are merely ignored. The next issue is that a cross structure function is not a rigorous mathematical tool. It follows from equation (1) that the temporal Dp({right arrow over (x)},0,t,τ) and spatial Dp({right arrow over (x)},δ{right arrow over (x)},t,0) auto structure functions at |τ|→0 and |δ{right arrow over (x)}|→0 are the first-order finite approximations of the respective temporal derivatives and spatial derivatives in the direction δ{right arrow over (x)}. The first order approximation of a cross derivative at |δ{right arrow over (x)}|→0, |τ|→0 is:
                                                                                                              ∂                    2                                    ⁢                                      s                    ⁡                                          (                                                                        x                          →                                                ,                        t                                            )                                                                                                            ∂                    t                                    ⁢                                      ∂                                          x                      →                                                                                  ≈                            ⁢                                                1                                      τ                    ⁢                                                                                        δ                        ⁢                                                  x                          →                                                                                                                                          ⁡                                  [                                                            s                      ⁡                                              (                                                                                                            x                              →                                                        +                                                          δ                              ⁢                                                              x                                →                                                                                                              ,                                                      t                            +                            τ                                                                          )                                                              -                                          s                      ⁡                                              (                                                                                                            x                              →                                                        +                                                          δ                              ⁢                                                              x                                →                                                                                                              ,                          t                                                )                                                              -                                          s                      ⁡                                              (                                                                              x                            →                                                    ,                                                      t                            +                            τ                                                                          )                                                              +                                          s                      ⁡                                              (                                                                              x                            →                                                    ,                          t                                                )                                                                              ]                                                                                                        ≡                            ⁢                                                -                                      1                                          τ                      ⁢                                                                                                δ                          ⁢                                                      x                            →                                                                                                                                                                      ⁢                                  {                                                            [                                                                        s                          ⁡                                                      (                                                                                          x                                →                                                            ,                              t                                                        )                                                                          -                                                  s                          ⁡                                                      (                                                                                                                            x                                  →                                                                +                                                                  δ                                  ⁢                                                                      x                                    →                                                                                                                              ,                                                              t                                +                                τ                                                                                      )                                                                                              ]                                        -                                          [                                                                        s                          ⁢                                                      (                                                                                          x                                →                                                            ,                              t                                                        )                                                                          -                                                                                                                                                                                                                        ⁢                                      s                    ⁢                                          (                                                                                                    x                            →                                                    +                                                      δ                            ⁢                                                          x                              →                                                                                                      ,                        t                                            )                                                        ]                                -                                  [                                                            s                      ⁡                                              (                                                                              x                            →                                                    ,                          t                                                )                                                              -                                          s                      ⁡                                              (                                                                              x                            →                                                    ,                                                      t                            +                            τ                                                                          )                                                                              ]                                            }                                                          (        2        )            One can see from equations (1) and (2) that the increment Δs({right arrow over (x)},δ{right arrow over (x)},t,τ) corresponds to the first bracketed term in the derivative while the second and third terms are merely ignored. Therefore, the cross structure function is a truncated representation of the cross derivative ∂2s({right arrow over (x)},t)/(∂t∂{right arrow over (x)}).
These theoretical issues lead to serious practical drawbacks when using structure function-based data processing methods with monitoring equipment having multiple sensors. For example, in the case of an atmospheric spaced antenna profiler, the major drawbacks are as follows: (1) an inability to retrieve the vertical momentum fluxes, (2) a high sensitivity to white noise, (3) an inability to directly measure the correlation between noise from different sensors, and (4) an inability to provide more than one equation for each pair of sensors. These drawbacks complicate the operational use of existing data processing methods and cause degradation in the performance of monitoring equipment with multiple sensors.